Uniqueness of spaces pretangent to metric spaces at infinity
We find the necessary and sufficient conditions under which an unbounded metric space X has, at infinity, a unique pretangent space Ωˣ∞, ř for every scaling sequence ř. In particular, it is proved that Ωˣ∞, ř is unique and isometric to the closure of X for every logarithmic spiral X and every ř. It...
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| Опубліковано в: : | Український математичний вісник |
|---|---|
| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/169432 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Uniqueness of spaces pretangent to metric spaces at infinity / O. Dovgoshey, V. Bilet // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 57-87. — Бібліогр.: 12 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862632705647181824 |
|---|---|
| author | Dovgoshey, O. Bilet, V. |
| author_facet | Dovgoshey, O. Bilet, V. |
| citation_txt | Uniqueness of spaces pretangent to metric spaces at infinity / O. Dovgoshey, V. Bilet // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 57-87. — Бібліогр.: 12 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| description | We find the necessary and sufficient conditions under which an unbounded metric space X has, at infinity, a unique pretangent space Ωˣ∞, ř for every scaling sequence ř. In particular, it is proved that Ωˣ∞, ř is unique and isometric to the closure of X for every logarithmic spiral X and every ř. It is also shown that the uniqueness of pretangent spaces to subsets of a real line is closely related to the “asymptotic asymmetry” of these subsets.
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| first_indexed | 2025-11-30T13:44:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-169432 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | Russian |
| last_indexed | 2025-11-30T13:44:32Z |
| publishDate | 2019 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Dovgoshey, O. Bilet, V. 2020-06-13T08:23:45Z 2020-06-13T08:23:45Z 2019 Uniqueness of spaces pretangent to metric spaces at infinity / O. Dovgoshey, V. Bilet // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 57-87. — Бібліогр.: 12 назв. — англ. 1810-3200 2010 MSC. 54E35 https://nasplib.isofts.kiev.ua/handle/123456789/169432 We find the necessary and sufficient conditions under which an unbounded metric space X has, at infinity, a unique pretangent space Ωˣ∞, ř for every scaling sequence ř. In particular, it is proved that Ωˣ∞, ř is unique and isometric to the closure of X for every logarithmic spiral X and every ř. It is also shown that the uniqueness of pretangent spaces to subsets of a real line is closely related to the “asymptotic asymmetry” of these subsets. ru Інститут прикладної математики і механіки НАН України Український математичний вісник Uniqueness of spaces pretangent to metric spaces at infinity Article published earlier |
| spellingShingle | Uniqueness of spaces pretangent to metric spaces at infinity Dovgoshey, O. Bilet, V. |
| title | Uniqueness of spaces pretangent to metric spaces at infinity |
| title_full | Uniqueness of spaces pretangent to metric spaces at infinity |
| title_fullStr | Uniqueness of spaces pretangent to metric spaces at infinity |
| title_full_unstemmed | Uniqueness of spaces pretangent to metric spaces at infinity |
| title_short | Uniqueness of spaces pretangent to metric spaces at infinity |
| title_sort | uniqueness of spaces pretangent to metric spaces at infinity |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/169432 |
| work_keys_str_mv | AT dovgosheyo uniquenessofspacespretangenttometricspacesatinfinity AT biletv uniquenessofspacespretangenttometricspacesatinfinity |